# Graphical Residual Flows

arXiv: https://arxiv.org/abs/2204.11846 · HTML: https://mlsanity.com/paper/2204.11846/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 23 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Understanding and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [Graphical Normalizing Flows](https://mlsanity.com/paper/2006.02548/) (2020)
- [MintNet: Building Invertible Neural Networks with Masked Convolutions](https://mlsanity.com/paper/1907.07945/) (2019)
- [Faithful Inversion of Generative Models for Effective Amortized Inference](https://mlsanity.com/paper/1712.00287/) (2017)
- [You say Normalizing Flows I see Bayesian Networks](https://mlsanity.com/paper/2006.00866/) (2020)

## Built on by (most cited first, 2 of 2)

- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [Reducing normalizing flow complexity for MCMC preconditioning](https://mlsanity.com/paper/2511.02345/) (2025)

## Abstract (arXiv)

Graphical flows add further structure to normalizing flows by encoding non-trivial variable dependencies. Previous graphical flow models have focused primarily on a single flow direction: the normalizing direction for density estimation, or the generative direction for inference. However, to use a single flow to perform tasks in both directions, the model must exhibit stable and efficient flow inversion. This work introduces graphical residual flows, a graphical flow based on invertible residual networks. Our approach to incorporating dependency information in the flow, means that we are able to calculate the Jacobian determinant of these flows exactly. Our experiments confirm that graphical residual flows provide stable and accurate inversion that is also more time-efficient than alternative flows with similar task performance. Furthermore, our model provides performance competitive with other graphical flows for both density estimation and inference tasks.